Matrix-Weighted Besov--Triebel--Lizorkin Spaces of Optimal Scale: Boundedness of Pseudo-Differential, Trace, and Calderón--Zygmund Operators
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916731329445888 |
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| author | Yang, Dachun Yuan, Wen Zhang, Mingdong |
| author_facet | Yang, Dachun Yuan, Wen Zhang, Mingdong |
| contents | This article is a continuation of our work on generalized matrix-weighted Besov--Triebel--Lizorkin-type spaces with matrix $\mathcal{A}_{\infty}$ weights. In this article, we establish the boundedness of pseudo-differential, trace, and Calderón--Zygmund operators on these spaces. The main tools involved in this article are the molecular and the wavelet characterizations of these spaces. Since generalized matrix-weighted Besov--Triebel--Lizorkin-type spaces include many classical function spaces such as matrix-weighted Besov--Triebel--Lizorkin spaces, all the results in this article are of wide generality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19060 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrix-Weighted Besov--Triebel--Lizorkin Spaces of Optimal Scale: Boundedness of Pseudo-Differential, Trace, and Calderón--Zygmund Operators Yang, Dachun Yuan, Wen Zhang, Mingdong Functional Analysis Classical Analysis and ODEs Primary 42B20, Secondary 46E35, 35S05, 47A56, 46E40, 42B35 This article is a continuation of our work on generalized matrix-weighted Besov--Triebel--Lizorkin-type spaces with matrix $\mathcal{A}_{\infty}$ weights. In this article, we establish the boundedness of pseudo-differential, trace, and Calderón--Zygmund operators on these spaces. The main tools involved in this article are the molecular and the wavelet characterizations of these spaces. Since generalized matrix-weighted Besov--Triebel--Lizorkin-type spaces include many classical function spaces such as matrix-weighted Besov--Triebel--Lizorkin spaces, all the results in this article are of wide generality. |
| title | Matrix-Weighted Besov--Triebel--Lizorkin Spaces of Optimal Scale: Boundedness of Pseudo-Differential, Trace, and Calderón--Zygmund Operators |
| topic | Functional Analysis Classical Analysis and ODEs Primary 42B20, Secondary 46E35, 35S05, 47A56, 46E40, 42B35 |
| url | https://arxiv.org/abs/2504.19060 |